In the classical model of tile self-assembly, unit square tiles translate in
the plane and attach edgewise to form large crystalline structures. This model
of self-assembly has been shown to be capable of asymptotically optimal
assembly of arbitrary shapes and, via information-theoretic arguments,
increasingly complex shapes necessarily require increasing numbers of distinct
types of tiles.

We explore the possibility of complex and efficient assembly using systems
consisting of a single tile. Our main result shows that any system of square
tiles can be simulated using a system with a single tile that is permitted to
flip and rotate. We also show that systems of single tiles restricted to
translation only can simulate cellular automata for a limited number of steps
given an appropriate seed assembly, and that any longer-running simulation
must induce infinite assembly.